Prior to the 2011 M9 Tohoku-oki earthquake, subduction at the Japan Trench was characterized by M7-8 earthquakes, sometimes rupturing the same source regions (seismic asperities), followed by extensive afterslip detected by GPS measurements. A physically-based model consisting of velocity-weakening asperities surrounded by aseismic creep on velocity-strengthening regions (the ‘rate-state asperity model’) became the prevailing conceptual model for earthquakes in this region. Theory and numerical simulation indicates that velocity-weakening areas do not exhibit sustained afterslip, while velocity-strengthening regions do not accumulate stress interseismically. Here we demonstrate that the rate-state asperity model is contradicted by models of postseismic deformation following the Tohoku-oki earthquake: afterslip in the first eight months either occurred on historical seismic asperities or stress accumulated in regions surrounding the asperities. Unsmoothed inversions of cumulative 8-month postseismic GPS displacements that restrict afterslip to areas outside of historical ruptures cannot fit the data without afterslip exceeding the slip that fully relaxes the coseismic stress change. In contrast, similarly constrained inversions allowing slip within historical ruptures can satisfactorily fit the postseismic displacements. These results require a modification of the rate-state asperity model and raise new questions about physical processes and properties of the subduction interface.